Generalized Parton Distributions

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ISBN 13 :
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Download or read book Generalized Parton Distributions and Their Singularities written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\beta)/\beta$ rather than with the usual parton density $f(\beta)$. This results in a non-integrable singularity at $\beta=0$ exaggerated by the fact that $f(\beta)$'s, on their own, have a singular $\beta^{-a}$ Regge behavior for small $\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x, \xi)$ that are finite and continuous at the "border point'' $x=\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\beta, \alpha)$ into the "plus'' part $[f(\beta, \alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x, x)$ with the $D$-term function $D(\alpha)$.